geo and nb - Section 5.6 Geometric R.V.s The Geometric...

The Geometric Distribution also deals with successes and failures. Unlike the Binomial and Hypergeometric who deal with the number of successes in a certain number of trials, the Geometric Distribution looks at the time it takes in order to get the first success. Or, you could interpret X if X is geometric as the number of trials up to and including the 1 st success. Pmf of Geometric: Consider repeated Bernoulli trials with success probability p. Let X denote the number of trials up to and including the 1 st success. Then the PMF of the random variable X is: 1 ) 1 ( ) (    x X p p x p where x is 1, 2, 3, … And 0 otherwise. X is called a geometric r.v. and is said to have the geometric distribution with parameter p. Notice that this is the 1 st time where x can possibly trail off towards infinity. Before we had x limited by n, the sample size. If one were to draw a probability histogram of a geometric r.v. what would it look like? Here is the probability histogram if p=.3. I stopped at x=12. What is the probability of

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